#Exploratory Data Analysis for the Red Wine Quality Data Set by Joshua Maine ##10/6/18 ========================================================
#INTRODUCTION
This dataset interest me as its similar to some further data analysis I want to do on data on beer. My longest running hobby, for almost a decade, has been homebrewing, and there is more similarities to red wines and beer than whites.
#Univariate Explorations and Plots
To get an idea of the data and gain a better understanding, I’m going to work through a few Univariate explorations. I’ll start by getting an idea of the table structure and looking at the summary.
## 'data.frame': 1599 obs. of 13 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...The data set as 1599 records with 13 variables. Taking a full look at the variables, it has:
X appears to be the wine tested, the removal of name and other identifying information, shows this is likely from a judging or evaluation of the wines in the data set.
## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median : 2.200 Median :0.07900 Median :14.00 Median : 38.00
## Mean : 2.539 Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :15.500 Max. :0.61100 Max. :72.00 Max. :289.00
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000With all the variables, this is most certainly data used in comparing and evaluting different red wines. Looking at the summary data there are things I want to plot and get a better idea of how the data is grouped and to find any outliers for correction.
Most of the quality values exist as a 5 or a 6, so I may group these a little tigther to sort the standouts on both sides. Grouping the values by pairs to have below average, average, above average is shown below.
summary(wd$ranking)## below average average above average
## 63 1319 217Looking at possibly related variables for trends or relations seems like a decent assumption. I’m going to look at sulfur and acidity related values first. THe relationships between acidity and pH, sugar and alchol content, and alchol and density as I suspect density in this case is referring to the gravity value of the wine.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 7.00 14.00 15.87 21.00 72.00Limiting the x axis lead to removal of 40 records
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 22.00 38.00 46.47 62.00 289.00Limiting the x axis lead to removal of 41 records
The next few charts relate to the acidity measures.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.60 7.10 7.90 8.32 9.20 15.90
Limiting the x axis lead to removal of 10 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1200 0.3900 0.5200 0.5278 0.6400 1.5800
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.090 0.260 0.271 0.420 1.000Limiting the x axis lead to removal of 6 records.
The next set of plots deal with residual sugars, alchol, and density
Limiting the x axis lead to removal of 10 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.900 1.900 2.200 2.539 2.600 15.500
Limiting the x axis lead to removal of 20 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.20 10.42 11.10 14.90This is another measure related to sugar to alchol conversions in terms of fermentation potential and actual. The vinter would usually take an originial gravity reading and a final gravity, what I believe density to be, to measure fermentable effeciency.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.9901 0.9956 0.9968 0.9967 0.9978 1.0037The last group of variables or other measures that initially I do not know or have any expectations about their respective values.
Limiting the x axis lead to removal of 59 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100
Limiting the x axis lead to removal of 16 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.740 3.210 3.310 3.311 3.400 4.010
Limiting the x axis lead to removal of 18 records.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.5500 0.6200 0.6581 0.7300 2.0000#Univariate Analysis
#Template Questions #————————————————-
##What is the structure of your dataset? The Red wine data set has 1599 items and 13 variables for each entry, one of which is a simple numerical listing of all the entries. There is one subjective value, quaility, which is how the wine was judged based on its othere values. The rest of the data set is composed of the chemical measurements of the wine. The data doesn’t contain one variable that may become a lurking variable, taste notes. I
##What is/are the main feature(s) of interest in your dataset? The features that have my interest relate my an existing hobby and area of interest I already have. I’m more interested in the fermentation related data including sugar, alchol, and density. My other area of interests is looking at the quality scores given and how it relates to the other variables.
##What other features in the dataset do you think will help support your
##investigation into your feature(s) of interest? At this point I think there will be common trends in the wines that fall into the 3 different ranking groups. Using the chemical properties, I suspect some things will be found to be indicitive of an above average wine.
##Did you create any new variables from existing variables in the dataset? I created a ranking of the quality values into 3 categories of below average, average, and above average. I may have to create more once I get into the bivariate exploration.
##Of the features you investigated, were there any unusual distributions? Quality, density, chlorides, and volatile acidity have more uniform distributions. Both sulfur measures, sugar, alchol, fixed acidity, and sulfates have a some sort of leftward skew. pH right skewed slightly right. Surprisingly citric acid has a flatter but still slightly skewed left distribution.
##Did you perform any operations on the data to tidy, adjust, or change the form
##of the data? If so, why did you do this? The data appears pretty tidy and easy to work with. I haven’t had to change any forms yet but have to do some adjustments to compare some values more easily.
#Bivariate Plots Section
Next up, I’m going to compare different chemical properties against the subjective quality measure and against other chemical markers.
Seems a bit too tidy and ordered, going to jitter the plot to so the density of the data a bit better.
That is better in terms of relecting the data in each category.
I find it interesting that it appears the above and below average rankings had both have a more narrow band in their repective alcohol content.
I’m going to continue plotting out the various sets I’m curious about.
I’m going to add jitter properties to plots that appear too clustered and possibly some trend lines if they make sense for the data points.
#Bivariate Analysis
The first set of information that I want to check is the correlation values between the campared values. Using a pearson method caluculation as shown below I’ve calucated all the below values.
I’m going to have to use the raw quality scores that ranking is derived from.
##
## Pearson's product-moment correlation
##
## data: wd$alcohol and wd$quality
## t = 21.639, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4373540 0.5132081
## sample estimates:
## cor
## 0.4761663##
## Pearson's product-moment correlation
##
## data: wd$alcohol and wd$quality
## t = 21.639, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4373540 0.5132081
## sample estimates:
## cor
## 0.4761663##
## Pearson's product-moment correlation
##
## data: wd$pH and wd$quality
## t = -2.3109, df = 1597, p-value = 0.02096
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.106451268 -0.008734972
## sample estimates:
## cor
## -0.05773139##
## Pearson's product-moment correlation
##
## data: wd$citric.acid and wd$quality
## t = 9.2875, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1793415 0.2723711
## sample estimates:
## cor
## 0.2263725##
## Pearson's product-moment correlation
##
## data: wd$residual.sugar and wd$alcohol
## t = 1.6829, df = 1597, p-value = 0.09258
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.006960058 0.090909069
## sample estimates:
## cor
## 0.04207544##
## Pearson's product-moment correlation
##
## data: wd$residual.sugar and wd$density
## t = 15.189, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3116908 0.3973835
## sample estimates:
## cor
## 0.3552834##
## Pearson's product-moment correlation
##
## data: wd$alcohol and wd$density
## t = -22.838, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5322547 -0.4583061
## sample estimates:
## cor
## -0.4961798##
## Pearson's product-moment correlation
##
## data: wd$chlorides and wd$sulphates
## t = 15.978, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3282127 0.4127694
## sample estimates:
## cor
## 0.3712605##
## Pearson's product-moment correlation
##
## data: wd$free.sulfur.dioxide and wd$sulphates
## t = 2.0671, df = 1597, p-value = 0.03888
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.002643125 0.100424406
## sample estimates:
## cor
## 0.05165757##
## Pearson's product-moment correlation
##
## data: wd$free.sulfur.dioxide and wd$total.sulfur.dioxide
## t = 35.84, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6395786 0.6939740
## sample estimates:
## cor
## 0.6676665Below is a table of the Correlation between data variables.
Variable 1 | Variable 2 | r | Strength | -/+ Alcohol | Quality | 0.48 | Moderate | + pH | Quality | -0.06 | Weak | - Citric Acid | Quality | 0.23 | Weak | + Sugar | Alcohol | 0.04 | Weak | + Sugar | Density | 0.36 | Moderate | + Alcohol | Density | -0.49 | Moderate | - Cholrides | Sulphates | 0.37 | Moderate |+ Free Sulfur | Sulphates | 0.05 | Weak | + Free Sulfur | Total Sulfur | 0.67 | Strong | +
I am surprised by a few of the correlations. The free sulfur dioxide and total sulfur dioxide have a strong positive relationship that isn’t surprising as its measuring the same chemical compounds. Citric acid and pH don’t have a relation to quality scores, so I can assume the judges probably had no biases to these qualities of the wine.
Sugar and density and alcohol and density both had moderate r values but the measures had opposite polarities. Sugar being the fuel for the yeast is responsible for both measures and their directions. Density is the relational measure offermentation potential and the goal range is 0 or below. Alcohol is less dense than water and sugar so a negative value denotes higher conversion. This is also shown in the moderate to strong negative correlation between alcohol and density with a r of -0.49, meaning more alcohol means a lower density but sugar leads to a higher value.
It’s an interesting note in trying to objectively explain the judges quality score, that judges statistically are more inclined to rate a higher ABV with a higher score.
Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?
My main point of interest are factors that may show trends in the taste judging of the samples. It seems most chemical markers have insignificant relations but there was a significant r in correlating alcohol with the scores.
Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)? From my own interests, I found the mathematical relationship that shows the sugar, alcohol, and density interesting to see charted out.
What was the strongest relationship you found?
The correlation of between sulfur measurements.
Multivariate Plots Section
To start off the multivariate investigation, it seems sound to some matrices plots and look for any additional investigations that haven’t been apparent to me so far. I’ve created a subset to exclude the sequential sample numbers of the wines X.
nox <- subset(wd, select=c(
fixed.acidity, volatile.acidity, citric.acid, residual.sugar, chlorides, free.sulfur.dioxide, total.sulfur.dioxide, density, pH, sulphates, alcohol, quality, ranking))Using this subset the matrix is as follows.
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
## [13] "ranking"
I don’t see anything thats super unexpected. The residual sugar and alcohol both skew the same as expected. The citric acid to sugar distribution is a little wider than I had thought but that sharp decline on the tail is interesting, so I’m going to add that to investigative plots.
From the previous data explorations, the first relationship I want to look at is the one between residular sugar, alcohol, and quality/ranking.
That isn’t a view that is easily readable by most, so if I use the hard set ranking categories it may translate better to the veiwer.
Ok that makes the rankings stand out a bit more and also shows that above the entries judged with a higher score overall plot higher in alcohol.
I want to explore some of the more posible complex chemical relations. Im just trying out a some different combinations looking for things that stand out. The citric acid and sugar relation caught my eye in the mass plotting so I want to investigate that.
Interesting view of two no related chemical markers in respect to quality score.
Well that doesn’t really show much. I’m going to keep exploring different measures to quality.
That’s more like the views Im hoping to find. Going to note that the highest sulfur samples happened to rank in the top group. I restricted the axis for better presentation so those values were lost.
Multivariate Analysis
Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?
The scieniftic explanation of alcohol, sugar, and density plot out nicely as expected. It appears that there are trends in higher rated wines, may not a chemical composistion but just the quanity that lead to a better taste experience. Knowing the quality ranking criteria and categorical scores but be a great data point to have in furthering this investigation.
Were there any interesting or surprising interactions between features?
The overall measures of most chemical existing in higher rates in the highest rated samples has my curiousity peaked in this data. Maybe scores can’t be factored out into key points, simply the higher content but still in relation to the other compounds make flavor even more complicated to account for.
Final Plots and Summary
Plot One
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
## [13] "ranking"
Description One
This is the overall scatterplot matrix for the data set. This can be argued that it may be very audience specific to the inclusion in presenting data with this added to it. For those that understand what is shown it adds an overall insight to the relations explored.
Plot Two
Description Two
This plot helps point to a recurring trend that higher quality wines average a lower resisudal sugar content. Some assumptions can be made to that line of thinking that could open a deeper analysis with a more robust data set. If I was the vinter of some juddged wines and had additional data such as age, grape variety, and other variables of the winery, this could help me improve the quaility or drive to better consistent products that are likely to be favored in judgings.
Plot Three
### Description Three
This a related plot to some of the other discussions showing ‘dryer’, lower sweetness, and higher ABV measures tend to be favored more.
Reflection
I found this data set interesting but maybe a bit incomplete for the questions it aroused in myself. My largest interest is how this can be used to find the factors that impact judging of the wines. There were some trends and relations that were found that helped shed some light on the question at hand. The most common factor seem the concentration of compound including alcohol tend to score higher. This could be due to several factors that prompt further discovery. I feel that having the values that were judged to get the quality scores, as well vinter specific inforamtion such as region, yeast strain, grape variety, and age could really round out the picture of what goes into making great wine.